1. Field of the Invention
The present invention relates to photonic crystals and methods for fabricating photonic crystals.
2. Description or the Related Art
Photonic crystals are of great interest in the field of photonics because certain types of photonic crystals exhibit a photonic bandgap. The photonic bandgap defines a range of frequencies at which electromagnetic wave is not permitted to propagate it.
Different types of photonic crystals are proposed and tabulated on page 862 in Baba, xe2x80x9cSemiconductor Micro Resonators and Control of Natural Emissionxe2x80x9d, Solid State Physics (Japanese), vol. 32, No. 11, 1997, pages 859-869.
The typical photonic crystal is a spatially periodic structure. One well-known photonic crystal exhibits two-dimensional periodicity in which multiple elongated, e.g. cylindrical, elements made of a dielectric material are in a two-dimensional periodic pattern with their longitudinal axes parallel to each other.
Joannopoulos et al., xe2x80x9cMolding the Flow of Lightxe2x80x9d Photonic Crystals pages 124-125, discuss the case of elongated elements in the form of air columns in dielectric along with a photonic bandgap map for a triangular lattice of air columns drilled in a dielectric medium having permittivity 11.4. FIG. 6 of the accompanying drawings illustrates this photonic bandgap map. It also considers xe2x80x9choneycomb latticexe2x80x9d along with a photonic bandgap map for this structure. This photonic bandgap map is presented in FIG. 7 of the accompanying drawings.
Referring to FIG. 6, the photonic bandgap map for triangular lattice of air columns clearly indicates that for r/a around 0.45, the triangular lattice of air columns possesses a complete band gap for TB polarization and TM polarization for frequencies around 0.45(2xcfx80c/a), where r is a radius of air column, a is a lattice constant, c is the speed of light. A complete band gap of the triangular lattice of air columns occurs at a diameter of d=0.95a, at a midgap frequency of xcfx89a/2xcfx80c=0.48, where xcfx89 is angular frequency. Thus, this structure has very thin dielectric veins of width 0.05a between the air columns. To fabricate such a structure with a photonic bandgap at xcex=1.5 xcexcm would require a minimum feature size of 0.035 xcexcm, where xcex is a wavelength. Such fine feature size may be fabricated, but this is very difficult.
Referring to FIG. 7, the photonic bandgap map for honeycomb lattice of dielectric columns clearly shows a large overlap of photonic bandgaps for TN and TE polarizations, around r/a=0.14 and xcfx89a/2xcfx80cxcx9c1, which is of much larger extent than the complete band gap of the triangular lattice. To fabricate such a structure with a photonic bandgap at xcex=1.5 xcexcm would require a feature size of 0.45 xcexcm. The production of such two-dimensional honeycomb lattice is less difficult to fabricate,
An object of the present invention is to strengthen such a lattice structure having a complete band gap, i.e., an overlap of photonic bandgaps for TH and TN polarizations.
Another object of the present invention is to provide a method of fabricating a structurally strengthened lattice, which is suited for mass production.
According to one exemplary implementation of the invention, there is provided a photonic crystal comprising:
a plurality of elongated elements formed of a first dielectric material and arranged in a two-dimensional periodic honeycomb lattice; and
a second dielectric material surrounding said plurality of elongated elements and extending between said plurality of first elements,
said second dielectric material defining between said elongated elements a plurality of spaces filled with a third dielectric material,
said first dielectric material having permittivity that is greater than permittivity of said second dielectric material and permittivity of said third dielectric material.
According to another exemplary implementation of the invention, there is provided a method of fabricating a photonic crystal, comprising:
providing a substrate;
forming within said substrate a plurality of elongated elements of a first dielectric material in a two-dimensional periodic honeycomb lattice;
forming a layer of a second dielectric material over said substrate to a thickness such that said second dielectric material continuously extend between said plurality of elongated elements, said second dielectric material having permittivity less than permittivity of said first dielectric material.
According to other exemplary implementation of the invention, there is provided a method of fabricating a photonic crystal, comprising:
providing a dielectric substrate,
oxidizing said substrate inwardly to define a plurality of elongated elements within said substrate, and
controlling the depth of oxidation of said substrate to determine dimensions of each of said plurality of elongated elements.
According to a specific aspect of the invention, there is provided a method of fabricating a photonic crystal, comprising;
providing a substrate;
forming elongated bores within said substrate in triangular lattice; and
oxidizing said substrate inwardly to define a plurality of elongated elements within said substrate until a portion of said substrate on a line segment interconnecting centers of the adjacent two of said bores is completely oxidized.